{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "10887fd7",
   "metadata": {},
   "source": [
    "# 模型选择\n",
    "\n",
    "视频：https://www.bilibili.com/video/BV1kX4y1g7jp?spm_id_from=333.999.0.0\n",
    "\n",
    "4.4章节：https://zh-v2.d2l.ai/chapter_multilayer-perceptrons/underfit-overfit.html \n",
    "\n",
    "\n",
    "·由于不能基于训练误差来估计泛化误差，因此简单地最小化训练误差并不一定意味着泛化误差的减小。机器学习模型需要注意防止过拟合，来使得泛化误差最小。\n",
    "\n",
    "·验证集可以用于模型选择，但不能过于随意地使用它。\n",
    "\n",
    "·欠拟合是指模型无法继续减少训练误差。过拟合是指训练误差远小于验证误差。\n",
    "\n",
    "·我们应该选择一个复杂度适当的模型，避免使用数量不足的训练样本。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56b70790",
   "metadata": {},
   "source": [
    "## 一 笔记"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d503e29e",
   "metadata": {},
   "source": [
    "### 1.训练误差和泛化误差\n",
    "\n",
    ">·**训练误差：模型在训练数据上的误差**    \n",
    ">·**泛化误差：模型在新数据上的误差**  \n",
    ">例子：\n",
    ">>·在过去考试中的表现很好（训练误差）不代表未来考试一定好（泛化误差）  \n",
    ">>·A通过背书在模考中拿到很好成绩  \n",
    ">>·B知道答案后面的原因\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4324086",
   "metadata": {},
   "source": [
    "### 2.验证数据集与测试数据集\n",
    "\n",
    ">·**验证数据集：一个用来评估模型好坏的数据集（训练模型参数）**  \n",
    ">>拿出50%的训练数据  \n",
    ">>不要跟训练数据混在一起（未参加训练）\n",
    "\n",
    ">·**测试数据集：只用一次的数据集（选择模型超参数）**\n",
    ">>不能用于调参 \n",
    "\n",
    "\n",
    "\n",
    "### K-则交叉验证（没有足够多数据时使用）\n",
    ">·算法：\n",
    ">>1.将数据集分割成K块  \n",
    ">>2.For i = 1,2,...,K   使用第i块作为验证数据集，其余作为训练数据集   \n",
    ">>3.报告K个验证集误差的平均"
   ]
  },
  {
   "attachments": {
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"
    },
    "image-4.png": {
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"
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    "image-6.png": {
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l52hkXQMcfbIMS84Dobua6EMTFi8sjBF7JFkmMuBIz7rUPJSY1CHVBB0POOoPTLuIHyyT62Hhqp/Ua4mOSF+JFkoK1sX+1w4BBnIhUtaC4chXj++wCmH/SaahQ8S0bTLnkzXtS19Cn619grTMjOXloO2vX3r6X4/E5cWfbF124hCfaf1G1slaJvNrRtaZY+ZSpOqwNcw2lowOb650EKC9md7O15FK1BAq64szE3XQoEFuXAP1AtPlmUGIZIzlzxtvvOGsdViNMWjP7JM1aOoLnXPKZFErZkEG+xvjHnzFBR0D4tSpU6dOST36al4K5rKHQMmQdbAz1hbCTTfdNC0rjtqWY+lLAwH652233Rb35UQYHkkXVRp29pjfMVbBWigMDqKuwA6erx9MNTGpwzFlnFmuTA9n1mFY/2fgGZUI0nrw+qxZs9xaKkH0kax5UfAFmMyzpC2kbi57CJQEWaPHRcLIlkMN0rRpU/dJGOzk2SrD8iltBML6VVhYECWNg3TOrFOsjJTAg3H5zzVNE3Y9GAaJJ8tP41O+mgRqmB1rh0BJkDUTQ1gfOJuOT86//OUv2czS8jIEsoIA5JtqXKU2BWVC7rUpx9LGI1D0ZI3eb5NNNpENN9ww/s5r+Q+TvHXWWcetj1DLrCy5IWAIGAIpESh6sp4+fboj1d/97nduBD0lIhlE2Hjjjd1IegZJLKohYAgYAjVCoKjJms81DPwhaqRgf4PUGqHlJSJvpvE2bNgwp5+cXpF2miYCDMitt956Geli08zaohkC9YZAUZM15nX/93//J1tuuaVsscUWjrSztZcgZM2oOC8BRtPN5Q8CmK+tu+66aQ2E5U+trSaGQHIEipqsmWCAiR12pNiF5sLc7g9/+IPbeTw5zHa1LhHgRcri9+YMgWJCoKjJmoeWUXGm0ubK5pPdMho1alRMfcLuxRAwBPIQgaIma8WbadWQNeSdbYf9NqoQZpaZMwQMAUMgVwiUBFmzyliuyBrj/+23377aOsO5ajDL1xAwBEoTASPrGrb70qVLnYoFaZ1pvRtttFENc7JkhoAhYAikRsDIOjVGoTH+/Oc/u/UauIh0jakYaz7nQtUSWgELTIgAbTBs2DBri4QI2YVCRMDIuoatttdee8l+++0XS43N9XbbbRf7byf1hwALDP3+9783+/f6awIrOQcIGFnXEFTWd2YGIw6LExatYaBx3rx5NczRkmULARbvx87avnKyhajlkw8IGFnXsBWYJQc5s7sGZM1KZHvvvbew27i5+kcA1ZQ5Q6CYEDCyrmFrIrU1aNAgZgXCf3bvYGr7d999V8NcLZkhYAgYAuEIGFmH45JW6ODBg2XzzTeP042yzjW7RZszBAwBQyCbCBhZ1wLNX375xalC2NwAh3TN4uysR8L2SeYMAUPAEMgWAkbWtUASct56663dJqSaDfrrFi1aCLtAmzMEDAFDIFsIGFnXEskHH3zQrejnZ8Mmpgw+MnHGXN0jwCqIG2ywgVmD1D30VmIOETCyriW47BjDoCIE7bsmTZq41f7YqcZc3SKgdtbp7BVYtzWz0gyBmiNgZF1z7GIpW7VqJe3atYuT5FjrGt31559/HotnJ3WDAKqo8847r24Ks1IMgTpCwMg6C0AzQYbPbqRoiELdoYceWk1FotfsaAgYAoZAJggYWWeCVoK4kDRrgwTXo2DiDDPpJk+enCClBRsChoAhkB4CRtbp4ZQyVpcuXdx+jFiIqEPKvuGGGxxhE+Zf0zh2NAQMAUMgHQSMrNNBKY04ixYtchYg8+fPj8VWlQgqklztVBMrzE4MAUOgqBEwss5i8+62225y4oknxiRoJGn8O++84wYbbRp6FsFOkdX06dNj7ZAiql02BAoCASPrLDaTknLYbufsA7nZZptlsTTLKhEC7G7OEqm2mFMihCy8EBEwss5yq/3lL3+Rfv36VZPqUIkwUaZPnz5ZLtGyCyLw008/ObI2O+sgMva/kBEwss5y6w0YMED++Mc/xpnwaREvvfSSU4dAJuYMAUPAEMgEASPrTNBKI+6aNWuc9ceYMWNCY7dp08at1GeWIaHwWKAhYAgkQMDIOgEwtQnu3r27bLrppm6STDAfyHz99deXbt26BS/Zf0PAEDAEEiJgZJ0QmppfWLFihWy44YYye/bs0EwIZwBs2rRpodct0BAwBAyBIAJG1kFEsvT/hBNOkC233LJabmrOd+mll8of/vAHgdjNZRcBVTHpMbu5W26GQP0gYGSdI9zZmADp+b333qtmGQKJYB3SrFkz2XXXXatdz1GVSiZbTCe32Wab0EHekgHBbrToEDCyzlGTQsjHHnusYMqH86U8zvG//vqrW1Oka9euOapFaWb7ww8/mJ11aTZ9Ud+1kXWOmhcyZiEn1roOWyZVCVu3ARsxYkSOalJ62TIZpm3btqV343bHRY2AkXWOmhcyxh199NGxmYu6VkiwyIEDByYk9WBc+58eAvoyTC+2xTIE8h8BI+sctZGSNQSNdD1jxow4VUiw2NNOO80NOK5cuTJ4yf4bAoaAISBG1nXQCU499VQ3qzFZUZB606ZNZZNNNgm1z06W1q4ZAoZA8SNgZF1Hbcy6IMxqVIk7rFg2Mdhiiy1khx12SBovLK2FGQKGQHEjYGRdR+3bu3fvlNI1RI6Eza4zrVu3NsKuRdvYcrS1AM+S5iUCRtZ11CwQMbrrG2+8MWWJTElns92TTjrJbIVTolU9gi6RmmhAt3oKCzEE8h8BI+s6bKPRo0e7RZ5SLd0JsS9btsxtwnvuuefWYQ2Lo6glS5Y4O2sj6+JoT7uLSgSMrOugJ6ieGvL461//Ku3atUtZKnHZKgwJu1OnTinjW4R4BJYvXx4fYP8MgQJHwMi6jhvw008/deqQBQsWpFXyvHnzHGFfeOGFacW3SIaAIVCcCBhZ10O7HnXUUdKoUaO0BxCVsE8//fS009TDbVmRhoAhkEMEjKxzCG6irFlpj8HGwYMHJ4oSC0eFgo77s88+c+tgMyPSdLExeOzEECgZBIys66GpIeA77rjDzVhcu3Zt2jX4/vvv3aSZffbZx20Gq7rwtDMokYjgYtiUSGPn4W1q32P7vq+//jprfdHIup4amwkwDRo0kPbt26ctKdMJGDhj+c+///3v7ryeqp/XxYItLzRzhkBdIqBCAnutsvwxxgGHHXZY1qpgZJ01KDPP6OOPP3YN+u6776aVWDsD0vjuu+8uG2+8sTBQaWqRePjUzjqTr5b4HOyfIZAeAvrs8Sxj5cUOUWzbx/hS2Gqb6eUaHsvIOhyXOgmloc844ww3xVwbPZOCO3To4OyJX3zxxUySFX1cSLp58+ZZ+/wsesDsBjNCQJ/Vb7/9VliLnjXrWU5it912k8mTJ7sxpowyTDOykXWaQOUqGsTC4k3XXXddRkWolP3II4+4jtK5c+eM0ltkQ8AQyAwBnrmlS5fK7bff7uZLQNANGzaU//znP257Pn0m9ZhZ7qljG1mnxijnMSZOnJiR7bVWSDsFliLox/72t7/l7K2uZdrRECg1BLDeQiji+YKgN910U7n++uvdTk9goc8hx1w6I+tcoptB3oceeqj7nNJPrAySuqgMqrFBL6TNxBtzhoAhUHMEVq1aJSNHjnQEjZktm1tfcsklblA/16ScqNZG1omQqcNwGh91CIMTdIiadAbSQPSk5+2PLrwm+dThbVtRhkBeIcB2cMOHD5fNN9/cPUOsfnnmmWcKJnj54Iys86EVRBzRTpgwwS2P+sUXX9S4VhD2Rx995Eak+WzDNrvUHBiw/6U5QyARAggyeDatfuCBB5wZLULOH//4RznrrLPkm2++SZS03sKNrOsN+viCVQrG/GejjTaqtVTMrMeDDz7Y6cLvuuuukjLvQxL6/e9/Lyw1a84QCCLwww8/SN++fWXrrbd2zwcbfvTo0SNG0DVVRQbLyfZ/I+tsI5qF/BjAOOWUU2qdE3rssWPHOn0b+uyvvvqq1i+BWleqDjL4+eefbYnUOsC5UIqAfBnH6dixo/z5z392BA1R9+nTx61sWSj3YWSdhy2FGoRBjenTp2eFXBksOe6445wejg6Lbk4l+Ty8/VpXiXt76623ivoeaw1SkWeABcekSZPkn//8p1tDni8tbO8HDRoU00HnqwSdqGmMrBMhU8/h2F0zwIF0nA2nBMbgyQYbbCBMpCGsmEk7G7hZHvmPgPZj9Mz9+/eXnXbayQkm6J/btGkjo0aNKgoBxcg6T/siHZCNc9nxPNuuX79+Ttpo0qSJME3WnCFQCAgEBQssqKZNmyannnpqbBbhVltt5fTP7733XuyWNJ0eYxcK7MTIOo8bDPUF0kG2Nx6g02ItoaqRgw46KDa4ksdwpF21Qn8o077RIo4Y1oZ8ZTLucvPNN7up3agK+Urce++9ZciQIcJ2bqQLS1sMUBlZ53krzp492w2WIUHkwrGEI7o8Ov4JJ5xgK/nlAmTLMzMEoiKR8kr1H4PFI0aMECaNMTEF8zq2xuvevbuwAFqh6Z0zAyI+tpF1PB559w8poXfv3k6CWLlyZc7qN3fuXDcDkoEYJG427C1UxwN8zDHHFK2EVajtkk69MTn9+MO5ckaHDo6U6Y+YsiI9v/76624NDvJRCbpYpegwrIysw1DJszA6JLprdNi5dJTz/vvvu7WymbZ+4IEHxkbOc1lutvPW3c2xejGXnwgoyfJiZZnf8847z01Mod+tu+66ssM//iGPPfaYLFy4MCY9axr/jsLC/OvFdG5kXSCtif6az0CWRa2LDsrA43bbbefUIzvuuKOzR6XcQvjshKRZybAucCqQ7pNX1YSAzz777Bg5o4JjmdE777xTvvzyS2cBZW1XvcmMrKtjkrchSCB8FrIkY104HhhmA6IvpNw//elPcu+992bNnLAu7sHKqF8EGBRk+QPs+5mYBTHjmfjVq1cvmT9/vnupZstEtX7vNrelG1nnFt+s5z506FDX2dEx17W77bbbnO03gzz77rtvQeu16xq7Yi8PsuXljjndc88957azYscU+gpqDUzqVHJWLIhvErSikfpoZJ0ao7yLwSckE2aYpVUfbtasWdK4cWNXB1YKvPLKK50pYH0/fFFmZs6fL5GRI53nPFpeXh8QFW2ZqMFoZ46rV692W1f961//ElRlEDNSM+am7JryzDPPyC+//JIQCyPqhNCEXsg5WedDgxx55JFyzjnnFNVbfJdddnE6PySZ+nA8rEhTrFjGQjg8qGzkyy4ayR7QXNU1Mm2alF14oZSdcYaU33yz82Wnny5lXbpIZMaMXBVb1Pn6zy7EjI3z/fff76Rm1GK0OdIzmzezvZW/pRVWHYnGN/x8ixrALN9czsma+tLQyRrou+++y/JtxWdXjGTNIBqDMuzizYNRX07blam+SNgQN9IVC+WwstmiRYuStn026l0xaJCU9+ghUe/FxVcHdSOs/PLLpaKO9PzZuJ/6ysPhVTVhivVpBgwYIEcddZQbrIWYIWj0zphFPv74424ilbZ/ImKur3spxnLjyPqhhx5yHTwI/JtvvilvvPFGNU84fs6cOQkfSKQvGjyRo6wjjjjC7W2WKE5tw4uRrMGE/eCwELnooosSSjG1xS7T9Dy8EPQNN9wQsybhIWe351dffdXpuXm56EOeaf7B+JHRo6W8b9+4YIgaPalfRnmfPhJ55ZW4eKX2Bzx8z7PJpq8sGMZaNAcccIAjZIgZ/Hjhtm3b1knTOhBYapjl0/3GkTVTNpkQEZTUeJM+/PDDzg8cOFB8j3UAI72Qrv9w+J0C3RV2lMQJvgiuvfZaZ2Gg14L5ZAOsYiVrsGGkHTKkTXj48s1BnPSr/fbbTzbeeGMndSOdXXzxxTJjxgxhhhqO/hLsG6nuJbpwoZSFLCXLhgtgEsyvrF07iebhovKp7jOT62HPIM/zjz/+KIw13HHHHe4Zb9CggWsLvoJol0aNGsn5558vw4YNE2a1mss/BOLImurRWIbX08UAACAASURBVEw79js6pls0uB+mt8KDAVkrOWt4p06dRP25554rhx9+uFvjgjD0x+p5c2s8PfodTvOrzbGYyRpcmI6LNDRu3Li4F2ZtMMtWWu0XHOk/rCt89913u0k+DE4yCQJ1DkICJolI5elOZinv3l0q3n23WlUpa/To0dXCK956S8quuKJaeCEGKK5+3dn1BKJ94YUX3HRslgdlHAFCxvMVhn4ZrNE9z5w5M25gOCxPP387r18EqpE10hnSMoMJ6iC7oLSt19A3s0+Z39CcY5+rnhllnPPZ3rNnT7fPWfAab371mne2jsVO1uB0yy23OOKrzZZg2cI7VT70DxzkDbmg/zzssMOcbhSJGGLB1Ovoo4925l4ffvhhjFQ07+iSJVKWRL2m8YLHsiOOkGiVNB+8lui/9m09JoqX63DKh5Ax2wSzyy67zOHG5CWsg3jxgR3WGIQhRPFFjETNpCrwxtf3feQap2LNvxpZ05DaqHrTqEH4ZOVNHPToIZWsNX6yI/pptltK1GEIz7YrBbIGs8svv9x9/vO1kwscs90uwfwQFOgbTHln/AQJkHUhlIg4sq8kX3r3duwoi046yZmOoWpRYcK/b+1jflg5+v133gkWXef/tU4cuW+setQUjrXGefnyXDHln2UGIGBeZKpP5v8//vEPN6MVKZmF9ml38vLzrvMbswJzhoAjaxqXgQYam/3JkIDVQdyPPPKI22GB46OPPlrNP/nkk6Hki+oDolSPyoOwY4891o0o8xLAI0HhCc+FKVqpkDVtxqcvy0bqC1HbsZCP9AkkSgQF+h8k9u/mzeWhxo0dgSFNQuSYkbEi2x577OH6FeMkLKf5xBNPOLOyzz//XNbcfLOsGT7cqVpUtafklglGKtBwJB886hvqimcJWr46GXxHJcOYAvbI1J1noFWrVk4lAelSbwb0IGLug/Zjht+ee+7p9Mj33HOPG5xlkI8XE+VonSmfc/2fyT1Y3MJCwJE1D8IFF1zgPpvY2RcJTZ12BD1qOEfC/M4S7DB0WjqW+rffftvpqiES7dx6TY9+/tk6LyWypg0gAh522qZYXcVzz0nFHXe4vsVqhAgbLCPL7LmbbrrJ7VCNLbrOooMI8Q9sv71ctOWWjuS5hocc0Z+j04U88Qy6gWHQE460T1zSkBYPyUK4SL+oIyiLlwjnqp4gHS+S9u3by4033ijMRh0/frxb6hNiR1XBM1PM7Vas/bEu7quaGgTrAuxl1aEfQ5pBqk7kWR2LzhYka81DCR0pGsLG8bkW5jWups3GsZTIGrzAEJ0vUmYu8MxGm9Q2j8hbb0n5xRdXy0bvlw0bEABUeqavOYGgSxdZVTWwxpck0vYnn3ziTFCZ1PHaa6+5TYaRhhmoY/BW/ciRI90WUcSZMGGCezmw1yPp0b0zNoNEDekikEC8Wj71wpszBGqKQEqyZnQeiQVbTPWQH+fosfGcL1++PFaHgw8+2OkV0S2q5/McNcchhxziwjgm8nvttVcsr2yclBpZgxnEwE7OkHYxkkT0p5+krG3b0O6xePFiJzFDmNw7QoR6BhgjS5fG/mt4UNAgXTHiFgqYBeYNAsF+6FcslKzRrSVKhKTQrl270I6cKA0FnnHGGW7QyC882XmyvJKlC7tWimQNDkiSfLZjGZBNPMMwro+wMmYmVn2p+eWj1kM1Ebznitmzpdz7avTTBM9J6/vgdftvCOQCAb7iErlqZI3awydr/Zzjkw7PtGImNBAe9IkKQepGqoboU3nyCD5kifJNN7xUyRp8aCOWNmXSA6qAYnLRr7+WspNPrnZL9J8wqbjsxBMlunhxtfgWYAjkAwKJ+q3WLSlZk9i31sBig5FsteiAgDGvwnMeRrKEoe5gMgTpMd3Dc66qEc2DYy7Wkihlsqah0aFuvvnmwm7mvCzD2kk7RKEdI2PHSnmvXnHV5v6C90icyLhxcfHsT90iEGyTdEuvabp0869tvGzWj3GRREJVSrJWKw3V4bETNkTLCDxhVNT3wRvHXO/WW2+Ni0N8SJldT6iYptcygnnU9n+pkzX4QdibbbZZURJ2xeOPS3m3bhJdvbpaVyGs/NJLpWLIkGrXLKDmCGB1w4s/XcdzjlcDg2TpWEeG/qqOvRfTdXBJ2FcV6ZVnEh0TlUG9u3TpkuiyC2caPyaitXUszYH5dJgLJWusQbDphOSYyagkymJOEDUDOEjBQVAAQR1gI5WzGwTx9JoCRR40ioZrulwcjawrOypqLKYbo8NGPVIX2OeiPcPyjMyc6ZZDLevQQcr79XO+7LTTpOziiyUye3ZYEgurIQKQ13333ecMBTA9VB4I9ifWfWGht/79+zu+4Iv6qquucurUREWzndypp54aJ11ipJCuY613zCKDDtPkNm3aCMYPYb5169bBJLH/3B+TlNh8I3iPROI6Qmk2HNZFiVw1sgZciPjEE0+MWXhQGdQYgI2jwqxbzKQDzn3PdUyeAJi3BA3rX9dzJGvIWvMjnHI0vruQpR8j6/8BCUk3bNjQWYnwdQTuxeLYaCD6+edu44HyF16Q6BdfSLTI9PT51lYYDhx//PFOEoYk+c/SATz/rPUDT0ydOtUJBzzf+ER9jvCTTz45ttWX3itq1DCnnBG8xsSjSy65JC6YlSkxryRN0BMRAg86OAqhUicMQsgs56DhmCvjsZvnS4N46jP56giWm+h/NbLmrQbA6pYtW+YGHKkoNqTcKA5SZeF5JG0+bXwAmFTDTCsaBhD0jeab6qGvplEJU/M+PXLz2XRG1vFo0i5MVWbgkS8gbdP4WIX7D4kOaxD6qLncIkDfYU0fHBvhojbFIdwhJdLXcMlI2kUQcTbsCIDBdgsja8plQbDggl3al7FYY9lXdRhFYBzB9aAnThhZo/qA5LHZ57xz587uPwvTwYdI63jCiUPdWbkQzyxwrYvWobbHamStGwVQEHum8dbkUydRwbx5eJtCvhpHj1ROzznqebDSek2Pweu1/W9kHY+g4tyyZUs3Ew9Tt2JykAczCYMPfTHdY77fCzyCMKZknaq+fPFhuOAvIKdpwsj6gw8+cPH9+R0anyOSrV82ZA1Xad/3j8QPI2vikEfQs9Adywdw3XfBPP1r2TivRtZ+plq4HxZ2Hqx0WJz6DDOyDkefduNBYJo0M/nyvR3D76J6KPfBanPFcj/V77B+Q9Ar+0SYqDa9e/euJvmGxSUvVgjkOUVVEXRBsmbFTlSy8+bNi4tKe/vev4j0q1/zvER8T/4YToQ51MKzZ8+O8winr7zyitPH63VWNlTPCyQXfS8pWYdVvhDDjKwTtxqdikEZ1rFgpmouOlni0u1KISJAf0G3jFoUR59BV8scDd+ziBUrKDIdH2LFv/vuuzFVCen4+mEA8rTTTnMDi8nIGmmZr0Ce5/feey/WV7XPYj6M+oPxNuKk80JJhT8LgWHpoR5tA0TP0fd6nWPY10GqctK5bmSdDkolEAfzSgibdWCy0clLALKSvkXIGdUBm4jgMCrA0kM9E+uwKrviiivckf+oIpBucUqwGCGg/oC0GS8LIzqVrBmLQFfMC0DT+3kxTqaepWVrowYjfzx5+B7pOZ0xNU3vbjZLP0bWWQKyGLJhqisrxPGAmTMEUiEAIfnLKStBBY/kQxhEi2TsCwNI1OirccnIml2QUH34Rg7J6ueTNXXEeIGXCx7yJy/9r0ffsAIJX78G/CMWbKhA/K8F/7qec517zqYzss4mmkWQF6P4SNh0dnOGQDYQgLRQUbBaYdD50m8YWZMWtQP9UUmesFRE6JN1sEz+q46a8slX8+Ya5wwisj+seixLsHJDvcI5O15dc801Cb1viRJWfk3CjKxrglqRp/nll1+c6RsTaFTqKaRb5kEeNGhQIVW5YOsKsbE0bCJHW7CnKwO+qRzqBV9n/eWXX8pRRx3lpGImdClJ6zFZfqnIGnWMT9DJ8tJr1G/s2LGuHr5qRK/n+mhknWuECzB/HgYGc1j8iUX2sU8tJIc+FdM9tfktpLoXWl2vv/56N/gWNgkEMmTAb/DgwSklYe5byRrbfwYwIWpIGp02TkmaI07JVv+7wKofn6yx3sDaRD2TZpD0UWkQxoCpXktkxsr65QxcMtkG3TtHPPtgdu3aNc4PydHSBkbWfgvbeRwCPAQ8MKhFsLUvFMdELnZx0Ye5UOpdiPXUWc3BuqvVBiSHCyPUYBola8KRYNVBvDjyCOaD1B5GsKTR9uc6X4h47L/ZhhB1Bl+QzOLVaxyDLx3K4+WPKoZ8EFyw19bZi+jhmdHoewZCc+GMrHOBapHliYkSA4+M9AcfliK7VbudDBBAx4w1hzqIDtO8YcOGucFEJieFEazGDx59suaa9jUGB/W/hul/hImwiTFK1ux8xWbCWg+OECwvEWYaos7w83QFeT+QM8SOSWJYXEhc6xJ23cuq1qdG1rWGsDQywPgfabV58+amXiiNJk94l5AbK8OhnvCJjoXb2NwXciNcfcKMAhcyJWvIEcsOvw6aJQTfo0cPp07R6xyZos5AIWnZb/bZZ5/VJLEj13Cs94FuG8sOnObj/lT9KFknuu7Hre25kXVtESyh9HzeNWjQwG0Yu2DBghK6c7tVHwFIizWBtA/wH7M3vsBwrAmCTvizzz5z/32SQzXBfz9M8w6StYYr+SuJajhqCcjSz4tzbKF5kaDu4D9lMn4BebMsM2Hq0akz8YX/fv7cH2aF6My5DyaMsSBV0FPOxIkTnUeCVz9lyhSXp9Y1G0cj62ygWGJ50MHRY//nP/8psTu32wUB1sVAKlWH+gN1hDqID8mbhY2QcP2F3LBp9qVRP00ismawkXx4AfiefIYPH65ZxI5YlCBYUA9eKFdffbWrg1oIEe67m266ydWJhelwXNeXCv9nzpzpJotx3/6m4Vi4DBgwwOHBNd/zbATL8cusybmRdU1QK/E0dMKhQ4c6wkb/l+1OWeLwFsTt+2RGhcP0xsE4xKOvhPUXwrCiYNAv6LiG1MtLAUlXfTCe/1/LoQ7vvPNOjHzDyiZv8rz//vtjg5J+XpyTjrzUaz5aTqJjMJ/a/Deyrg16JZyWzsngC8ussgMNI+b54hjhZxszfaDypV5WD0OgNggYWdcGPUvrpB2W0V1vvfViOsv6hoVPcLOzru9WsPKzjYCRdbYRLcH8kGDZ6HOdddaRVq1aOVvW+oSBT1UWDjLJuj5bwcrONgJG1tlGtITzY3R+yy23lPXXX9+NipcwFHbrhkDWETCyzjqkpZ2hSrVMomF2Gf/NGQKGQO0RMLKuPYaWQwgC7Oax0UYbuV1osFM1lUQISBZkCGSAgJF1BmBZ1MwRYNEcbLKxlfUnHWSeU+Yp7AWROWaWIn8RMLLO37YpippBmPPnz3dSNtPV2eg01yRK/m+88UZR4Gc3YQgoAkbWioQdc4oABHrBBRc4ixFWamMSQq4cKhhM91hhzZwhUCwIGFkXS0sWwH0w2Mgu6ltttZVbFOqll17KyQAks+DYsd3Wsy6ATmFVTBsBI+u0obKI2UIAKbtv375O+m3RooVbGzjbqhHWJjZnCBQTAkbWxdSaBXQvkDPqitatWzspmP3s6noAsoDgsqoaAmJkbZ2gXhGAtNkVRNcYefnll2P1yba0HcvYTgyBAkTAyLoAG63YqgwpI1UzRRwzv6ZNm8bWSi62e7X7MQRqioCRdU2Rs3Q5QYCdsvfZZx9H2qxdXJsZkCaZ56SJLNN6QsDIup6At2LDEYBg8QsXLnTLnGKC169fv/DICUIxC/zb3/6Wc3vuBMVbsCGQEwSMrHMCq2WaLQQw72MyDd7XZyfL//vvv7clUpMBZNcKEgEj64JsttKqNKqQPn36uNX8tthiC2HH6mSO+Gx0as4QKCYEjKyLqTWL/F6Y5HLOOee4jQ6YWLNo0aIiv2O7PUPgfwgYWf8PCzsrEARWrFjhdq9ms4MmTZoIG6SaMwSKHQEj62Jv4SK9PwYhf/zxRznooIOEtbObN2/u9oQs0tu12yoABHJtfWRkXQCdwKqYGAEeEDbr3X///R1pt2zZUj799NPECexKnSJQUwIjXaK0c+fODb2HZcuWZXW1Ra1D8BhaeNUO6Kx9k8zclNUg2VGpJs7IuiaoWZq8Q4AHit3WDzvsMGej3bhxY5k9e3be1bPUKnTcccdVIyfaar/99ksIBdfPPffc0DGJVatWyVFHHRWa9umnn5Z77rkn9FowkOUNsOn3HeXeeeedctddd7kj50F/++23+0mqndP/EB4SubZt27pNphNdTxZuZJ0MHbtWkAh88cUXjrBRj2BvPWrUqIRSWkHeYAFVml2CWBIXAoMMcRzbtGkTdxfnnXeeWytGr1944YWOrImr6bg2YsQIueWWW2JhzHzlOtLsGWec4RYFI0zD9Rr/fceL/cgjj5Qvv/wylhdxqeucOXPknXfekbfffruaP/TQQ2Px/fy0jj/88IPwguK/euqGv/rqq+Xuu+924fzXNH4+yc6NrJOhY9cKEoGff/7Z2VmzVOrll1/urEc23XRT6d+/f07X0S5IsHJcaQjpq6++csRIe+AIqwlZk07JkvNJkyY5KRvSPfroox3RQraHH3547Jz/XD///PNj5Km3zAuEa999912sXvxP5g455JA4kqUefCUQfvDBBztPHfGYj3JkXIVr/Ceefz1ZWcFrRtZBROx/wSPAA8TEGHXl5eXuc3aTTTZxxN2lSxf57bff9LIdc4wA7cFuQQ888IArif81IWv0wZhuIpWiDvHdhx9+KEjnKlUHj6TBUbY6zj/55BNBGtZrStYq+RLH90Gy1nTB+IQ/9NBD8vjjj8fy1rI1P3chg5+SIGverjSygpUBPha1iBDggXrhhRfc5geoSJB4+EzHWd/IXUMrOSnGtEOmZE0a9L0sJUA+SMojR46MESlqEwYeiYdPx4XVC+kXVcUdd9wR6sPIWssL5nf66afH1Cx6TevFf02nYamORtapELLrRYcAD8q8efNk3333dbrtBg0aOF0ok264Zq72CKDyGDNmjPOMGcyYMSOWKSSVKVlPnDjRbQtH+yxdulSOOeYYlx9WQOSFRMzgnqoaErUjZQ8ZMkSeeuop54cNGxYjfDLk5c0MWSRu+kjQcy2YN/9Rc0Dk1AXPfwZCUXlomIaruiQGSJonRtZpAmXRihOBlStXuqVZ11tvPTedHWmISTe44ENZnAjk5q5QQw0aNEgeffRRwYKiZ8+esYIgTAjLd8kGGIkHGeMPOOAAR4AMAtI+5MV66DfccEMsuzDpN3ZRxNXrySefdCoKJX1ta47JPPnodc3T3z6O+uBRy5x11lkapdoxmEe1CCEBRtYhoFhQaSHAg4OOc8KECW4TBFb6a9iwobz22msuvLTQyM7dgqk6drTHVE4dWGdC1uSlYwwff/yxnHTSSTF1CHlifYEZHiSJQ7r2y9dy9aiEyouatDjis3NRhw4dUvrp06cnzZ/8unbtKuPHj9cis3I0ss4KjJZJPiGAXpMNDGrieGixDoAQWOkP4j7zzDNt892agFmVJkjWSKKMF/gumWRNm+DZV5N0SsqETZs2zREuZnaQKEfImsknvvfL0nPIGisSHHnhqJvvKc//zzkD1hpfLUGQ5tXzIkK/rmoZVXuoFYh/pK7pOiPrdJGyeAWDABISJMuDVVv3/PPPC2Z/arP93//+N0YWtc27FNJDagz8+WoQJOsDDzww7vZTkTVpkHrBH7KEsDkOHz5c/v3vfztLk4cfflgGDBjgTPewPMFjkYEPc1iUoAahjkq+es5x9erVcdf1Wlheftgll1wi9913nx+UlXMj66zAaJnkEwI8xMxgzKZjKjMmf0jbbD0G2TDYpJ/U2SyrmPKC4JCsfbLm/jJVgzAQyIDdCSec4KRrLLzQiZM/RO63A5KrEmuyFzaSOmStkjoDl75n2YKOHTvGhXEdO35NE2wrNs1At84AK30Gz3nQE075mTgj60zQsrgFg0Cih6mmN+CTweTJk91A17rrruskbgaSFi9eHJPOalpGMaYLkjX/wRI1AefqUknWqBQeeeQRN/ireWgb89LUWYPkp2QNiVNOIqdkrfW44oorBN+jRw/nzz77bDe5JhjO/+D6HuRBedQTS5KLL77YvdwxMezcubN70WBeqJ4wBka17ER19MONrH007NwQSBMBJQymP++4446OtDfaaCP3Sc4kCyX3TB7GNIsuqGjcvy9Zo5pYvny5k5B9bBKRtd6sErOmQWJmBiLhEDWzJNUpWfMfM73u3bu7S5pW4/lkzTXy8uNA9JdddpkzPyTc95qHHiFq9gwdOHBgrO01P45Ysej/ZPlofmFHI+swVCzMEMgAAR4+yIPp7KxFwjrbf/rTn6RXr15udpw+nBlkWTRRuXfM2FCDtG/fXi699FLp27evIzX/JlORtWI4a9YsOe2009zA4Lhx45zOmiUFfKdkDTniUJkEJWHCIevjjz9epk6d6myhqac6Bicph8Fq8sOcU8lW4+iRMRIGF1lESuNofTniUPtofTRdpkcj60wRs/iGQAoEIIZbb71V/v73vzv99mabbSa9e/eOW4NCH+IUWRX8Ze7zsccec3pcBgdVVRDUJbO/JtYZONLoQk4KAGQOIWJPzTrmOCTrMDO9IFmruZ/mpUcW/EIPjm094xw4ymYCDwSvOmXUGkjZmAcG2w0bcnTUU6ZMcdcgZN9rfKxKOPe9lqf1SXU0sk6FkF0vSATQIdenUymKwSgkSbYhY2Dyr3/9q9OLLliwwBGXPrz1Wddclg0OLKykq9thWgcRhjnFgmOQrBknwHFNj0wJZ/INLwDfKVlrftTh5ptvjqXVuBD/0KFDXTh5IFlD3HwBKFFrXAYbeTGw4h/StrpXXnklRsDdunVzUjjlq1dzPsiec/LwPaaD2lc0z0RHI+tEyFh4wSLAyDume/pg1/WNKEnokYcRjyUBBIPEjSngH/7wB0cOb775Zkyyq+u61kV5fGlw/+Dx7LPPOp11onIVMwYTacdkjrgqEbMCHwQJKV555ZUxAtX0xA06rRPXkL4xuWO6OeFhjrKoFyqN4AvCz0vvId1jWFlhYUbWYahYWEEjAClC1okeuny4OWbkPfPMM7L33ns74t5ggw2c3pQF9FERhJFLPtS7ruqgRFeT8pQ4a5I2Fe61ybsm9fHTGFn7aNh50SDAkpypHrx8uVk+qxnQwoaYl4xOwLnooovidkvJ55dPvmBZzPUwsi7m1rV7KxgE9MUCIaOHve2224T1tyFupO7WrVsLE0PUaXz9b8fiR8DIuvjb2O6wABFAJwpxM9CFPhZbYkwCGaRE133KKac4k7MCvDWrcg0RMLKuIXCWzBCoSwRUV8p6FZjC7bzzzo68kbzXX399N2OOQTKcSd112TJ1V5aRdd1hbSXVEQKlQFaqv2aNCWy62UAB4kb6xrMz0syZM2NWC0r2ddQEVkwOEDCyzgGolmX9IoCJFba9peiYMHLTTTdJy5YtncQNgbOGCcu8vvjii0ln4pUiXoV0z0bWhdRaVte0EGBtjmwtkZpWgXkSSb8oOKrkzazAO++805kIsnYJuCB5N2vWzC3jySw+VCu+I73m5Yfbef0iYGRdv/hb6TlAgHWKt9tuuxzkXLhZKgEzcMlqb6wUiOoEfbfqvU8++WT5z3/+I8yuDBJ44d558dTcyLp42tLuxBDIGAEkcMiZRaiY+vznP//ZqU0g8C222MLtIs7kHZXAia9Se8aFWYJaIWBkXSv4LLEhUPgI+GoTzpmkg2UJU+OZWo29N+oTdN/smsOUbnZkee+991xcnfINEqY+yV1/MLLOHbaWsyFQsAggPfvEi+77888/dyTN0qGbb765s/nG7ptJO40aNZILLrhAnnrqKRcPAvclcD+vggWlnituZF3PDWDFGwKFiAC6byRwrE9YV5rdy9nqTHXgKoXvtNNO0qlTJ3niiSdkzpw5hXireVNnI+u8aQqrSLYQQIrzpbps5Wv5pIcAi1SxRO2oUaPccrD77rtvTA+OLhxVCkvGslQom90S7+uvv04v8xKOZWRdwo1frLfOGtJIdr4utVjvtRDui5cnnt1WWPeEyTr333+/Wx6WLdF0Ig9ttvHGG8uWW27ptsFiH8PHH39cWAPb35hAp+LzQuZc8y8ELGpTRyPr2qBnafMSAT7NGRDjITZX/wgomeqRGvltwzlETrux+uBDDz3krFBYPna99dZzZI5ETpsy2MnWabvvvruweww25M8//7ywOYD/NeXnH0Qg2bVg3Hz6b2SdT61hdckKAjyM77zzTlbyskzqBwElVJWekazZjGDatGly9913S8eOHWWfffaJ7XmJdK6DnSx0paoWLFfY9JYXALu6zJ07V5iiX4jOyLoQW83qbAiUOAIqRfukjtoLfTnSOeoTdn457LDDpEmTJk69ouoWJXbULmqSiASPhct+++3nJgz16dNH2AiCCUTkxz6M7KDOzuz15Yys6wt5K9cQMAQyRgByVoLWY8aZVCWA8DFHZLNebMqR1hn03G233dwMWPTnSuioYfBI73gIn/+qpiFMLWH8lwJ7OmbLGVlnC0nLxxAwBIoOgWQvBK6xvyS7EiF9jxkzRtjB/cknn5SHH35Y2PmcndKz5Yyss4Wk5WMIGAJFiQCknIy0uemw62FhtQHIyLo26FnavEQAcy5m02X7YcnLm7VKlQwCRtYl09Slc6NqugdpmzMEigUBI+tiaUm7jxgCjNhvttlmcXa3sYt2YggUKAJG1gXacFZtQ8AQKC0EjKxLq73tbg0BQ6BAETCyLtCGs2obAoZAcSCQ7kC4kXVxtLfdhSFgCBQAAhCz75kx2bNnT2HxsVSuJMia9QFYUzf4BvNBS3SeCkC9TnpmROk0WA1PdUxUroanSu9f1zR69K/551ynnhov1VHvK9UxUT5h6cLihsXzw3RBez8seM596mp7wWvB/9Qh8CHE0QAAF0ZJREFUHZduvHTysjiGgI8Ak2dYZZCZkttss42MHDnSXQ7rcyVD1mxPxC4WzC569NFHZeDAgdX8I488Ir4nzj333OM8i8ck87fddpv06tVLevfuLawrgOecMN/fcMMNct111znPG/Wqq65K6P/1r3+5RWi6du0qqTzLSbIJ6plnnhnz/A/z7PTB5qgnnnii8yeccIIcf/zxof64446TQw891Hmm4rLWQiLPusUsrpPKs5oaU3pbtGghzZs3d57znXfeuZpn8Xp2IWEDXHzDhg3jvIZzpLPT8VmVjanAHP/6178m9OwxmK5n3Yh0/F/+8hdJ17PfYbqehYnS9axMl45nOjU7nqfj//jHP0q6noWU8BtuuGGo1+sc2WUmHc9Ubjxx9Zyp3mGeOIRDgEHvx9ep5KwPol6nlet/jhrGMfjfv+af65RznZ6uU9Q1PNGReJRx0kkn+ZzuzkuCrCFIfSj1geM/DzIPNwuhb7311kk9O0FDBok81zUfJRCIZfvtt4/zhOn1bbfdVho3biw77LCDO3Luexag0f+cN2vWLKlv2rSpQG6Q3q677iq77LJLNe8TpBIlxJnMkwbfsmVLtzQly1OG+VatWgmea61bt3Y7h7B7SJg/4IAD3JrFbdq0kcMPP9xt1sqGrb4/5phj5NhjjxWOhPPiaNeunevIdGZeOKeccorz7du3lw4dOggvIl4+dPrOnTun5Vnwp1u3bkl99+7dpUePHsIL9Oqrr3Y7o1x77bUS9Cymj6fP3XLLLc7feuutksyzzCd7Gj744INJ/QMPPCCDBw+WIUOGOMED4SORHzp0qLDR7YgRI9LyLFj06quvul1f2Pkl6CdMmCATJ050fsqUKTJ16lTnp0+fLnimVbNONdOuZ82aJbNnz5a33nrL7dPIXo0ffPBBzPNfwz788EPBz5s3TxYuXOg8Cybh2ZDgm2++iXkN/+6778T3rJGNbT1+yZIlsnTpUqdWQLWgnhX78Ky4xxRx3xOmHrNP9RqmR81D89HwVEcti0WmfE84WMIHkDcvt0svvdTFqcbUIlISZB124xZW3AiMHj065zfIp2pNVSs5r5wVUBAI8PWHgPPDDz+krG9JkjUPmfqUCFkEQ8AQMARyjECYjjpYZEmSdRAE+28IGALZQSAqUYlIhUREqnxUmPTPf3O1Q8DIunb4WWpDwBAIQSASicqkC6+QyPJlIpFyo+sQjDINMrLOFDGLbwgYAkkRcBaRUZFhu7WWkU32FilfIUjc5mqHgJF17fCz1IaAIVCFgKo+HC9HIjL89lvl1cMOF4muEInaCoi17ShG1rVF0NIbAoaAQ8An62g0ItHVy+WVZq1k1dwPnWStg/phR4MwNQJG1qkxSh3DvvBSY2QxigyBiDeIWDmAiOys8jPHMonIzKtvkFnbNZeKZb+IRCOhHmI3lxoBI+vUGCWNQT+zrpYUIrtYRAggl+Aj9PvyMlnzymj54Jrr5Y1OF8qbHTvLmx0vkDlndZY5p58nM09sL2P2OlAmNN1FxjZpIa802lleadRCXm28s4xr1ELGNdpZxjTeTV5utCv7YlVbDqKIYMvKrRhZ1wLG8hWrZOip50o0YqJ1LWC0pIWIQFRk8PYHyltbNZcZDZrKpG13ksVdL5aFXS6Uz7qcL59f1EUWXXmlLHr6efn588+k7NelUv7rL1L26y9SsXK5VKzC/yblq1bLil+WVUrchYhDHdbZyDpTsD1eHtfrenl5jwMkWh6UrTFVqnJV34bO6D2yRuS35SJlJo4rPHYsPARUupZIVFaXl8nasrVu8axotEwqVRpIySLRciGKRMvU5ppjpfpEhGek8mEyLUh6fcDIOj2cYrGUlleu+FVeaba/lH27oLoepKo301nxdMr3XhonT+y8r0zebg9H1hVprvgWK9hODIF8RIC+zkNRJX9EpHISDMprVCVl1LlCZK2IrKnyLszFVw13Pt5Y/tXJyDrNNqnsj1W9sqJCpjdpKd/36S90TpUQXFbub1S+vfdhWdK5h7y6VXN5fccW8vQOe8r4e+4RqYjIWtfB+TFnCBQhAnTttavkp163y4p+d4p8+62Ma7ybTNt2J5m8VVP5rcsVImWrivDGc3tLRtaZ4BtBEojINfseKK8fdIjI2kil5FCVR3k0KkOuvEkm7LCnjN2hiYxpsouUDxhIz3Uff0gXpF/NwSTrKtTsUGwIYFI9s19/mbTtLjKx8V6yYvxEmXDwUSJLfhB5+wN5caeW8vSxJ4lUUx8WGxLZvR8j63TxjFRS7ut7tpHXtm8qq1f8JlJJu7EckLtnD3tZfn72aZm8bVNHyKzKFqX3louU/bpMXj3ocHmv578lUs5HoTlDoPgQQA75dtobMn675lK+pqzywxNpu4K5MRFZu3KlTG26p8gqk64zaX0j6zTRKo9E5fbTTpFJOzaTGTu0kElN95DomIlxqemP5VIhP0+bJlO2beRUHjEtSUTk12lvuHQ/DXlOpLyqE8crUeLysz/pIZDOimWaUyZxNY0dM0Eg6vTXFVGRl5rsJD88/KRIZK0w+Li6YrWsfP9dGdByd3m93VkiZSawZIKskXUKtNxsKxEZd0hbmd54R5nQqIUsHflfGdvhHPnk7Asqbaw99TPx37y+r3zQ+vCqofBKNkYFsvyz+fL6jruLRFdXSt2E/bhUouUVBbt2QllZWWwroiCUzz//fFzQCy+8EPc/G39Y7F638UqVH20zbNiwVNFCr7t+4C2tm+p/aCalEuhmxKyRL194Sl7fbmeZf2YneW2HRjKpwXbyeuNm8uFd95pNdQ36gpF1EtAYPFz10Sfy6F77yOimLaT8JfZHq9RbTzy9i8w77dxQsn7+yBNk8Z33VuqlIfJopaHS2jW/yTM77SyycoVEkMGXLJNhLfeTL0cgoXuMn6RO+XZpxYoVbseWMPJi+y/CcRzZ9SUYT++HbdHYmuyiiy6KHTnv0qWL+88OGjh28fj44481mdslhp07fBcsQ/+jkjrvvPNkzJgxLrqGB49+XnrOvRx55JFyxBFHJPXsesP2Z5RV2i4qj7fcUyY03kUmbN9MIk8ME/n8S2crEmWkB3xc36jqH/8zKlHjktKGL+TujaxDQCEoEo3K2J7XyeTGu8m755wnFRVrvc4VkYkdLpRP2p9TjaxJ+9whh8m3Tw6tMvSnM0ac6VK5rJQBhxwk43fZXcY3bCGzttlBJp90usjaFQVL1itXrnRkzX1DemypxdZabLcFwXHOllunnnqq+892XFzjuKpKZ0k6tl9iqyb2kPz000/dVk6LFy92xPftt98KnnhsD9WvXz93TpnkxbZKvrvxxhvdNlp9+/aN7YWpe2NeeeWVbpswroVd9/P28zzkkENif6lHMseelaniJEtf8NewrXYYVchPc9+XFw47QWY12kvKvl3inheuuesBGAkrj0akLIrFVIUTiwoeiyzegJF1GJgRkUXTZsi4HXaVRQ895mYoxp5P18EqyXreqeFkPbzNIfLdsOecWV8FUsR338mMa3vJiB13k1G7tJDxTXYWGfyklK1YLRKpqJw4EFaPPA9DekSyhoz1AUQtglpi7dq1bm9F/qtnU17InXTE0TR6m/w///zz3R56KpkipeL4j2e/vptvvjmWNoyseUkQ7/3335c5c+bE/LvvvuvOOXINr/sBcmQfQeqoZWu9OFIP9oA86qijUnr/i8LPo5TOlYexkHIdfNlykTXljqzdHANmwlRUiPzws8inn8nyUWPko363yhvndJZpZ50r0886TxY/NkiknGdEcyslBKvfq5F1dUwq3+jsr4cmmX7i9xXXcSIyCTVIMrJ++lmZ+eBjMq7tqTKpUQuZte/h8u27c1xeHzzzokxqsqfIyjJBW+0WuAmpRz4HsWs6UvPpp5/uyItzPE7JDinbd2xwCyFXVFS4o3+Nc66hpmDDU85x7EqPy4Ss2YRXHfmwvx3EjOM/npfFf//7X3euebOBKXWkfkEHAfvptX7BeISXsmRNq1XNRqiEhj90cQeeyEejR8prnTrJa012lukNdpCZW24vb2y1g0xt3FxmH3u8vNPtMpnTs6e8d/VVMr5ZS3mj6T5S4WbRBJEuvf9G1um0uU/WEnUWHy8de5J8c/7lblZWHJmLyLA2h8uUZrvKqF32kO+xs170vRtErNzuiC2PKuTZSy+XqU1aify8HAZxXbyQFmhHT/zTTz+5XalRaaDGUJJF+oRkUR1AXEileuQc3a9PdgsWLHBh6LS51rZt25j0io5Yw4gH6aaSrNlJHEcZ1Iv6oGLxHdfYTRxpmXuBsNesWSPsIK4vGz8+eVAPrQt1DPNcJ25YHn5+xXZOD6Yb4xFAItEycRL0vHnyziXdZWyz3WV0k53lv7vsLm9edpmsnP2myE8/SVnZaimv4CurktXdr8usEqGXdt5dZLWxNWgYWWf41Li1DVhYvfGuUvbIU3GTYjSr4QcfKV+1PV6m7NBS1v64VMqj2IJUroqgv/Tq19ufIxOa7i5ly36r5Ht6amztBM0tf49IoHfddZcbcNNaQoKQFUeVUDlXT1giNQHSLuQJaSrZQfqk4T95oLNORdbUBdULqhAI9ccff3TVI/3MmTPlwgsv1Oq6Fw4vkPvvv9/lH7sg4l4+c+fOFTzlputVvUL5S5Ys8bMsunO6rPol8z8RWbtafvt1mQw99HAZ13hvmb7VrjL30BNk8eSJEl2zXMqdsBM3nFMpdmsmnmAUjZbL/QfuJT89O6rocKvJDRlZZ4gafSoaiciUbZqL/LLUdVQ/C66P79VXJv9jZ1n98cdSUVEmZbKqioJd6v9Fj4iMufIqmdx0D1kzYozrwdpXiVkIDjJE3dGpU6cYOUPWzz77rDz33HPuyLl6VA8QMMQZdIQFiRyJHMc1PLrlPn36xMLCdNZcxIoESR0duTq+BKgb0nrQcQ+odPQFw/X58+cL5obcB2aI1B2v9+Ifn3nmGVFPuMb/6quvgkUV1X/t0WVLf5GJzfaQ15vuKVMa7SpTr7hKyhd9K5EyJGzGG5C2achK7/p3sAt41wGJCTTDd91dyhcWN4bpdggj63SRqornOlkkItP/sYvIql9DU2OW9+KpZ8r0RvvJvD73VPZOpwcltcuhMl3V2MvXE16XaY13l/euvjF2VdcmCy0gTwKRXiG5du3aOV3zF1984QgV8zWsNxYuXCiQle+x8EhE1t26dZMRI0bEEfmBBx7o7lbJmj9I4DjCwsj66KOPdhI/1zUeqg5UFNRp6tSpbvDTJ2biYQny8ssvuzT8qDQ/adIk6dWrV8yyhPOgx9pE/U033ZRQnRLLvEhO6M2g/O5/X5KJLfeUqd26SdnnC6WcTXK9gUEdBQgeXWLNRDGpIvHPnhoiE7dqXrlKpV4r4aORdYaN70g0EpGp2zUXWb60WmrX7yqisioisvyjeXLPHnvJlOb7Vn3qcfV/fq37KKzsvtFlv8rAVnvIyG1aiKzCTLBa1nkVABGOGjVKRo8eLSeeeKLT+2JJgYOsEznSQcBKpBpvyJAhMfWJhnFUsvbD0D+jXsDzsvjtt9+q5efnP2/ePEfU33zzTSwbbLVRf/iSd+yidwJhUzfuU61a9HjHHXfI2LFjXTgvEA3/8ssv3cuLtFjF+HXxsi6O06p+OqRzNxnf5TK3k3kZndfprqtuMdCXP+55jUxrvpdM27GlRKZMdRZRfn/niQDPZ3c/QH69qndx4JSFuzCyzhDESrKukFkNm4r8ujwudWWfrFqHL2jkQQ+Ep/mJMqCCJQhrqFZ2bA6kLJ/0ZkFIEpAQKhBM9xhg5OGC0AiHBPfff3/nGWTEt27dWg444ADnDzrooHjcolGnmghKukSaMmWKvPrqq06nDPnhPvvsM8FeumfPnjJ+/PiYfjsu06o/2FyrDh3S1Dw0LtL2JZdcUi1cr3N8+umn5bLLLhMm7qAvv+WWW5w/++yzY+EMaqpH6r7ggguKm6QVoMomkUFnd5Epl17uSLoqyHV393HDcqjR1bJs6Xcyu8V+Mm3rJvLbDb3kq/MvlRkNW0nF6PGVYz8kjIisqYjIc4MGyms7tBJZulIql6nUAkv3aGSdadvDyNGIzJ/JrEPtlpWZcAkCDggScSUsm/OpLJs+W2RllfTsR3aj6ViLVH1bxqXMrz+QNCoIJFPUIEEHKerAIJI2JI7kSVgYaWoYR9+T78iRI51aQfNQNQjXiOs7JfxFixY5/Td1Iz16ZKaao39WXTp6Zc6RztGVP/bYY66emofmS7qXXnoprl6UC3mPGzeuWvjXX3/tJOtg3TS/ojoiZEQiMuici2XaBV1FWBSkyvn9eM3UmTKtyW4y6d4HpJxNOByBi3ww8lUZu0sr958nZ83KX2XGie1l1ra7Stm331SatmqGJX5cx38w7DyeKJLj8b9JHRqPWY+ssFd5jM8LM6ayigp5aNe2MrHRfhJdubZqsk18PNISV/PM1yMDf5jFoYKAEKknagkGALGGUMuJoUOHSteuXePCuc7EFP/eeOAHDBggqBbwt99+u/NIsqQ/99xznTQLQSLBol/Gf/LJJ3H5zJ492+nEkfY/+ugj6dixowwfPjw24KeDhP4RoqZ84vJigdz9uj311FNy9dVXyxNPPCGDBw+WRx991Hmmw19zzTXyyCOPxMK49tBDD7nJPeTp51OU5wwcRiIye8Dj8spBbSW6NvBcVESc2eqTu+8tK/veLWvLIhLBVK8iWunLy+TJnXaV6IqorPh8gYxqvq9Mbv1Pif6wRCoiVXlF8v95qIu2NbKuS2KkYzvJstyNkCcj5WTX6qJjpCqDqdrEgawhRs4h4IcfflgGDRrkjpyjKoEEe/To4Qht4MCBot4vgwd+1qxZMn369Gr+vvvuk+uvv75aOHF1GrrmxRR21g8hP3TUEH0y0uQaahtNj/Tvx+ccU0LyXb16tTvyNYHH3A+9vf7XI/Hwfj6af7EeVyxeLJOatZJo1fhB7D4jEZk/9yOZ2rCljN5qVyewuGsQcAXmnWtlSLMWEl2GMFP5cqtwR77ASuBllwH/GFlnAFasA9YkDZ0zgtRMB0S6wJSpsCUGyMgn6yA+b7/9tpNUiYe5nF4PIzHC1Gs8jqg+IEQIW68Hj358/zwdsiY+0rSfLnh+zz33SP/+/WPSvkr/55xzjnsJce3OO++s5iH+YF7F+j+ycpWM2rGFLHr4yVi/RuBwX4r0/dWrpWLlyio8IrJybbn8+vYH8vRe+8lr+xzqzPRo12ikwpnGGlFX5wYj6wInzPp++HWAUeuBvhePlIx6QaVc1BUQ9vfff+901+7BrMI+GfmSF6vk6aQVLcc/+nn54ZA1K/kRFizD/+9L1n56Pcc+G68WKHpE2mfwkUk3YV7L0HyK/ajtoF+FStZOKIlEZW20XCYd20Em795aXttmJ7d86utXd5PyCiZBVbZRsWNUm/szsjayrpX0FyTrt956S7CSYHEnJWp9iCFPiLF79+6CeRsdl2udO3d28RmwDPPoxPHkmcgz0Kfl6ANBedhcd+jQwaXT9Uv8I9eIo3Xx85g2bZqz+9ZJMQxI+p5lW7E20YFKHbz0jywOpfUp9iPY8XL1MfTveW00InP6D5Sfn35eKj76QNaU/SZs6sFiT4X+lenfZ67O1wFY84ZBTfuADjCSHknzqquucqZ1wfz0IUatwSQTSJkJMqgKWOI0mWeBJcqB/BN5LESCZTIZB0JlIDRZ/sx0JC111Hryn+ni6MUh3DBdOmQeFu6H8UURrFdJ/i+PSHkVxrRVRXlEIuWRymOFPX/p9Akja3tZZZVMdIAunc5XV3GCJFxX5Vo51Um4wn/ejKQzevaMrP3OY+cZdR4jo+pkZJgYJrnqA+uo1GHHyk9gw8FwsD5gfSAf+4CRdZWeMh8bx+pkpGF9wPqA9gEjayPr2MCadgo7GkFYH8i/PmBkbWRtZG19wPpAAfSB/we2NlFgPirkVAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "87731ef1",
   "metadata": {},
   "source": [
    "### 3.过拟合与欠拟合\n",
    "\n",
    ">影响模型泛化因素：\n",
    ">>1.可调整参数的数量。当可调整参数的数量（有时称为自由度）很大时，模型往往更容易过拟合  \n",
    ">>2.参数采用的值。当权重的取值范围较大时，模型可能更容易过拟合  \n",
    ">>3.训练样本的数量。即使你的模型很简单，也很容易过拟合只包含一两个样本的数据集。而过拟合一个有数百万个样本的数据集则需要一个极其灵活的模型。 \n",
    "![image-3.png](attachment:image-3.png)\n",
    "\n",
    "\n",
    "### **模型容量**\n",
    ">·拟合各种函数的能力  \n",
    ">·低容量的模型难以拟合训练数据  \n",
    ">·高容量的模型可以记住所有的训练数据  \n",
    ">![image-4.png](attachment:image-4.png)\n",
    ">![image-6.png](attachment:image-6.png)\n",
    "\n",
    "\n",
    "\n",
    "### 模型容量估计（VC维）\n",
    ">支持N维输入的感知机的VC维是N + 1  \n",
    ">一些多层感知机的VC维是O(NlogN)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "668cc10f",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "---\n",
    "## 二  代码\n",
    "\n",
    "多项式回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ddfe8ece",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "080aff48",
   "metadata": {},
   "source": [
    "### 1.生成数据集\n",
    "\n",
    "给定 x ，使用以下三阶多项式来生成训练和测试数据的标签\n",
    "![image.png](attachment:image.png)\n",
    ">噪声项 ϵ ：服从均值为0且标准差为0.1的正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3baddff8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 多项式的最大阶数，20维\n",
    "max_degree = 20  \n",
    "\n",
    "# 训练和测试数据集大小为100个样本\n",
    "n_train, n_test = 100, 100  \n",
    "\n",
    "# 分配大量的空间\n",
    "true_w = np.zeros(max_degree)  \n",
    "true_w[0:4] = np.array([5, 1.2, -3.4, 5.6]) # 其余为0噪音项\n",
    "\n",
    "\n",
    "features = np.random.normal(size=(n_train + n_test, 1))\n",
    "np.random.shuffle(features)\n",
    "poly_features = np.power(features, np.arange(max_degree).reshape(1, -1))\n",
    "for i in range(max_degree):\n",
    "    poly_features[:, i] /= math.gamma(i + 1)  # `gamma(n)` = (n-1)!\n",
    "    \n",
    "    \n",
    "# `labels`的维度: (`n_train` + `n_test`,)\n",
    "labels = np.dot(poly_features, true_w)\n",
    "labels += np.random.normal(scale=0.1, size=labels.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0ddc2b63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[1.4651],\n",
       "         [0.2250]]),\n",
       " tensor([[1.0000e+00, 1.4651e+00, 1.0732e+00, 5.2414e-01, 1.9198e-01, 5.6253e-02,\n",
       "          1.3736e-02, 2.8749e-03, 5.2650e-04, 8.5708e-05, 1.2557e-05, 1.6725e-06,\n",
       "          2.0419e-07, 2.3013e-08, 2.4083e-09, 2.3522e-10, 2.1539e-11, 1.8563e-12,\n",
       "          1.5109e-13, 1.1650e-14],\n",
       "         [1.0000e+00, 2.2501e-01, 2.5315e-02, 1.8987e-03, 1.0681e-04, 4.8065e-06,\n",
       "          1.8025e-07, 5.7942e-09, 1.6297e-10, 4.0744e-12, 9.1678e-14, 1.8753e-15,\n",
       "          3.5164e-17, 6.0864e-19, 9.7821e-21, 1.4674e-22, 2.0636e-24, 2.7314e-26,\n",
       "          3.4144e-28, 4.0435e-30]]),\n",
       " tensor([5.9908, 5.2027]))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NumPy ndarray转换为tensor\n",
    "true_w, features, poly_features, labels = [torch.tensor(x, dtype=\n",
    "    d2l.float32) for x in [true_w, features, poly_features, labels]]\n",
    "\n",
    "\n",
    "# 从生成的数据集中查看前2个样本\n",
    "features[:2], poly_features[:2, :], labels[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0910cac",
   "metadata": {},
   "source": [
    "### 2.对模型进行训练与测试"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9b20d1d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 实现一个函数来评估模型在给定数据集上的损失\n",
    "\n",
    "# 输入（网络，数据，损失函数）\n",
    "\n",
    "def evaluate_loss(net, data_iter, loss):  \n",
    "    \"\"\"评估给定数据集上模型的损失。\"\"\"\n",
    "    metric = d2l.Accumulator(2)  # 损失的总和, 样本数量\n",
    "    \n",
    "    for X, y in data_iter:           #  取出样本(数据，标签)，分别赋值给X，y \n",
    "        out = net(X)                  # 将X放入网络进行预测得到输出\n",
    "        y = y.reshape(out.shape)      # 将y的格式与网络预测结构格式变得一样\n",
    "        \n",
    "        l = loss(out, y)\n",
    "        metric.add(l.sum(), l.numel())\n",
    "    return metric[0] / metric[1]     # 返回平均损失"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7db8667b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义训练函数\n",
    "\n",
    "# 输入（训练特征，测试特征，训练标签，测试标签，训练次数）\n",
    "\n",
    "def train(train_features, test_features, train_labels, test_labels, num_epochs=400):\n",
    "    loss = nn.MSELoss()\n",
    "    input_shape = train_features.shape[-1]\n",
    "   \n",
    "    # 不设置偏置，因为我们已经在多项式特征中实现了它\n",
    "    \n",
    "    #线性回归模型\n",
    "    net = nn.Sequential(nn.Linear(input_shape, 1, bias=False))\n",
    "    \n",
    "    \n",
    "    batch_size = min(10, train_labels.shape[0])\n",
    "    train_iter = d2l.load_array((train_features, train_labels.reshape(-1,1)),\n",
    "                                batch_size)\n",
    "    test_iter = d2l.load_array((test_features, test_labels.reshape(-1,1)),\n",
    "                               batch_size, is_train=False)\n",
    "    trainer = torch.optim.SGD(net.parameters(), lr=0.01)\n",
    "    animator = d2l.Animator(xlabel='epoch', ylabel='loss', yscale='log',\n",
    "                            xlim=[1, num_epochs], ylim=[1e-3, 1e2],\n",
    "                            legend=['train', 'test'])\n",
    "    \n",
    "    for epoch in range(num_epochs):\n",
    "        d2l.train_epoch_ch3(net, train_iter, loss, trainer)\n",
    "        if epoch == 0 or (epoch + 1) % 20 == 0:\n",
    "            animator.add(epoch + 1, (evaluate_loss(net, train_iter, loss),\n",
    "                                     evaluate_loss(net, test_iter, loss)))\n",
    "    print('weight:', net[0].weight.data.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f79aaf",
   "metadata": {},
   "source": [
    "### 3.三阶多项式函数拟合(正态)\n",
    "后期训练集与测试集上的损失小 \n",
    "\n",
    "后期训练集和测试集上的损失差异不大"
   ]
  },
  {
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   "id": "b7ed9c14",
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   "outputs": [
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   "source": [
    "# 从多项式特征中选择前4个维度，即 1, x, x^2/2!, x^3/3!\n",
    "train(poly_features[:n_train, :4], poly_features[n_train:, :4],\n",
    "      labels[:n_train], labels[n_train:])"
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  {
   "cell_type": "markdown",
   "id": "82f209c3",
   "metadata": {},
   "source": [
    "### 4.线性函数拟合(欠拟合)\n",
    "后期训练集上的损失大(损失几乎没降低）\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9be9eb7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "weight: [[2.67452   6.0490327]]\n"
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   "source": [
    "# 从多项式特征中选择前2个维度，即 1, x\n",
    "train(poly_features[:n_train, :2], poly_features[n_train:, :2],\n",
    "      labels[:n_train], labels[n_train:])"
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  },
  {
   "cell_type": "markdown",
   "id": "67bb58df",
   "metadata": {},
   "source": [
    "### 5.高阶多项式函数拟合(过拟合)\n",
    "验证集上的损失低于测试集上的损失，后期验证集上的损失变大\n",
    "\n",
    "后期验证集损失与测试集损失差异大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "eef00107",
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   ],
   "source": [
    "# 从多项式特征中选取所有维度\n",
    "train(poly_features[:n_train, :], poly_features[n_train:, :],\n",
    "      labels[:n_train], labels[n_train:], num_epochs=1500)"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "252fb376",
   "metadata": {},
   "outputs": [],
   "source": []
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